The veteran star was cast as former British Prime Minister Winston Churchill in West End drama The Audience, in which Mirren takes on the role of Queen Elizabeth Ii.
Hardy, who starred as Cornelius Fudge in the Harry Potter film franchise, appeared in preview performances last week (ends24Feb13) despite his injuries, but has since "reluctantly decided to stand down", according to producers.
The 87-year-old actor will now focus on recovering after cracking his ribs in the accident.
Stephen Daldry, the play's director, has wished Hardy "a return to full health and strength very soon", adding, "For him to have accepted this challenge at his age speaks of his courage and commitment to the theatre. That he feels unable to continue is a great sadness to us all."
Hardy's understudy, David Peart, will play Churchill until producers find a replacement.
The Audience officially opens at the Gielgud Theatre on 5 March (13).
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